text: The equation takes the same  form as an undamped nonlinear oscillator(with cubic potential) one can pretend that  is time,  is displacement and  is velocity of a particle with unit mass, then the equation represents the  energy equation(, where  and  ) with zero total energy, then it is easy to see that the potential energy is
  where  in motion. Since the particle starts at  for  and ends at  for , there are two cases to be considered.
  * First case   are complex conjugates and . The particle starts at  with finite positive velocity and attains  where its velocity is  and acceleration is  and returns to   at final time. The particle motion  represents pure outflow motion because  and also it is symmetric about .
  * Second case  , all constants are real. The motion from  to  to  represents a pure symmetric outflow as in the previous case. And the motion  to  to  with  for all time() represents a pure symmetric inflow. But also, the particle may oscillate between , representing both inflow and outflow regions and the flow is no longer need to symmetric about .
  The rich structure of this dynamical interpretation can be found in Rosenhead(1940).